The Big Rewrite

SCIENCE IS DEAD! LONG LIVE SCIENCE! SUCH MIGHT be a summary of Stephen Wolfram's much-anticipated book, the boldly titled A New Kind of Science. Rejecting the past four centuries of research as an intellectual dead end, Wolfram proposes to rebuild the foundations from the ground up, along the way resolving such niggling problems as the structure of space and time and the origin of free will. Within the book's 1,280 pages, Wolfram claims to have found the true basis for understanding the evolution of life, the nature of biological complexity, the mechanisms of fluid dynamics (one of the greatest unsolved problems in physics), the behavior of financial markets and the origin of the Second Law of Thermodynamics -- you know, the one that encodes the principle "Things fall apart." About the only thing he doesn't seem to have explained is how to make the perfect cappuccino -- and no doubt he could do that if he put his mind to it one Thursday afternoon.

The modern scientific landscape is littered with self-proclaimed reformers, most of whom are relegated tout de suite to the "round file," but Wolfram is guaranteed a hearing from science's top echelon. In the past two weeks, his book has received major press attention, from Wired to The New York Times to a Newsweek cover story. What sets him apart from the average reformer is his status as a bona fide genius. Publishing his first scientific paper at 15, Wolfram was only 20 when he obtained a Ph.D. from Caltech, where he studied with the legendary Richard Feynman and quickly turned out a series of articles on the foundations of particle physics and cosmology. At 21 he became the youngest person ever to win a MacArthur "Genius" Fellowship and, after a stint on the Caltech faculty, moved on to the Institute of Advanced Study, Einstein's old home.

Wolfram has endeared himself to the scientific community in another way too, as the creator of Mathematica, a brilliant mathematical-modeling software package used by scientists and engineers the world over. Mathematica has made Wolfram a rich man, enabling him to eschew academic life and to forge his own idiosyncratic path through the thickets of human ignorance. For almost 20 years he has been working alone on his revolution, refusing to publish until he had the full picture; continually delayed, the work is finally ready for public inspection.

And the public is ready: Pre-release orders put the book on Amazon's top few hundred for much of the past six months -- occasionally cracking the top 50 -- and within a week of its May 14 publication, the entire 50,000 print run had sold out.

The results of Wolfram's efforts are gargantuan in every way: The primary text alone contains 250,000 words, plus another 250,000 words of notes and almost 1,000 illustrations. A hundred million keystrokes were expended on the enterprise, along with "more than a hundred mouse miles." The research generated 10 gigabytes of storage and hundreds of thousands of pages of notebooks, nearly a million lines of Mathematica code and more than a million billion computer operations. Behind these numbers lies an equally dizzying claim, that science in general, and physics in particular, was founded on a delusion.

Perhaps the primary innovation of the scientific revolution was the idea that nature could be described by mathematical equations -- Newton's law of gravity standing as the archetypal example. From the subatomic to the intergalactic, equations are the lingua franca of physics and, increasingly, of many other sciences also. Economics, for one, is becoming virtually a branch of applied mathematics -- John Nash's Nobel was no fluke. So powerful a grip have equations exercised on the scientific imagination, physicists today dream of an "ultimate equation" that would encompass the whole of physical reality. Yet, according to Wolfram, this entire enterprise is fundamentally flawed --equations, he says, can never be the basis for deep insight into nature's workings. In their place he proposes simple computer programs called cellular automata.

Such programs are highly visual -- the output of a cellular automaton looks a bit like a checkerboard on acid. The basic layout is a grid of squares in which the color of each square (just black or white in most of the examples Wolfram considers) is determined by a simple set of rules. One such rule might be that if a square is surrounded by all white squares, then its color should become black, or if the square has a black square above it, then it should become white. The process of studying a cellular automaton involves choosing a particular set of rules, setting up an initial (usually minimal) arrangement for the starting grid, then letting a computer rip. At each "tick" of an internal clock the computer updates the color of every square according to the rules, thus creating a new grid arrangement, which in turn is further updated, and so on ad infinitum -- or until the operator gets bored out of his mind.

This may not sound like a promising setup -- and indeed most scientists assumed nothing interesting could come out of such simple systems -- but in the early 1980s Wolfram made a surprising discovery. He found that even with extremely simple rules, cellular automata could give rise to incredibly complex behavior; over time, sophisticated patterns could emerge, some of which seemed to mimic patterns found in biological systems. Many might have dismissed this as an interesting quirk, but for Wolfram it became a beacon, a sliver of light pointing toward a hitherto unexpected computational continent. He set himself the mission of exploring this land, which to his surprise turned out to be inhabited by a profuse variety of "creatures."

SPEAKING BY PHONE FROM HIS OFFICE SOMEWHERE in Illinois, Wolfram indeed likens himself to a botanist. There is no way, he says, to predict how cellular automata will behave; the only way to find out is to observe them in action. In short, there is no substitute for good old-fashioned fieldwork. Wolfram might be seen then as a kind of David Attenborough of simple computational systems -- over the past decade he has studied literally tens of millions of cellular automata (and their ilk) and has come to believe that they provide an explanation for many of the deepest problems in science.

Take the case of fluid dynamics: How and why water flowing around a rock breaks up into swirling vortices had been a major problem in physics for 200 years. Understanding such turbulence is of huge importance to ship builders and to the airline and automotive industries, for air is, in effect, a fluid. Reducing turbulence could save the airline industry alone billions of dollars annually. Using simple computational systems, Wolfram has been able to model fluid flow, and his methods are already being applied in high-end simulation software. But what interests him is not so much the practical spinoffs of his work as its theoretical bearing on the very foundations of science. As he sees it, cellular automata provide the true model for almost all physical phenomena: The markings of shells, the shapes of snowflakes, the branching of plants, the ontology of randomness and the unidirectionality of time are just some of the things he claims to find therein.

In part this book is an Audubon Guide, a lavishly illustrated watchers manual to cellular automata, complete with a detailed taxonomy and field notes describing the behavior of each subspecies. As with Attenborough, Wolfram (a London boy) approaches his quarry with a breathy English enthusiasm -- the spots on this one, the stripes on that one, it's all so endlessly fascinating! Yet Wolfram tell me he has only begun to scratch the surface of this new continent: "There's a lot more botany to be done," he insists. With this book he hopes in fact to initiate a sort of observational mathematics, a grand new science of the computational realm. Moreover, he believes this science will lead to all sorts of new technologies, and makes an analogy with a bioprospector trawling through the Amazon jungle for new pharmacological compounds.

Wolfram's ideas have already been instrumental in launching the fields of chaos and complexity theory and the discipline of "artificial life," but as they say in show business, you ain't seen nothing yet. Among his most radical proposals is a network model of space and time -- imagine a kind of multidimensional fishing net, itself reducible to a cellular automaton. Wolfram tells me he won't mind if his old physics friends "think all this is a bit nutty"; what he hopes is that a few serious people will take up these ideas and explore them in depth.

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Theoretical physics has always been a bit of a wacky field, and it's one area where Wolfram has some cachet, but other scientists may not be so sanguine about his incursions into their territory. It's a daring man who will refute, as Wolfram does, the mechanism of natural selection as a driving force in biological evolution. In a chapter of astonishing audacity (or is it hubris?), he dismisses much of the Darwinian canon, including the sacrosanct concept of maximizing ecological "fitness." It is hard to imagine that Richard Dawkins will take this lying down.

In 1638, Galileo Galilei published his great work Dialogues Concerning Two New Sciences, the book that in many ways launched the scientific revolution. Whether Stephen Wolfram can initiate a second revolution remains to be seen. Whatever its ultimate effect, A New Kind of Science reminds us that the line between genius and lunacy is fine indeed, and not always so easy to discern.LA

Margaret Wertheim is the author, most recently, of The Pearly Gates of Cyberspace: A History of Space From Dante to the Internet.